iMac won't turn on, help!

I just bought my brand new 27" i7 a month ago and I was so excited...now I'm nothing but annoyed and disappointed! Please help! My computer was having a lot of problems starting up, but I was going out of town and didn't have time to deal with it, so I just let it sleep. Right before I went out of town I powered it off, now it won't turn back on at all! I'm just 2 weeks out from being able to return it, but it's pretty BS that my 1 month old computer won't even turn on!

Any suggestions or ideas? I don't really want to get the logic board replaced - even if it is covered - on a computer I JUST bought...I'm kind of hoping it's a user-error, but not sure how that could be.

You are great!

The "unplug for 30+ sec" then "hold down option, command, P&R" worked - any idea what this could mean??

Do you think this is going to continue to be a problem?

Thanks again for your help!